Question $1.(20$ marks$)$

Answer $2coskg$

A $0\mathrm{.}9$ m radius circular control gate $AB$ is pinned at A and rests on a smooth surface at $B.$ If the water depth in the reservoir is $2\mathrm{.}9$ m $,$ and the weight of the gate itself can be neglected, calculate the mass of the counterweight that should be placed at $B$ to maintain the water depth in the reservoir at this level without the gate opening. The width of the gate is $2\mathrm{.}0$ m $.$ Assume water at $20C.$